Graph the inequality.
x > 4
Answer:
Step-by-step explanation:
Find the measure of 2.
50 2.
1130
< 2 =
[?]
Rackham Graduate School has 8,000 students (5,000 PhD students and 3,000 masters stu- dents). The Rackham Student Government Executive Board has 4 student members: a President, a VP of Operations, a VP of Finance, and a VP of Administration. Reminder: no need to simplify your answers in this homework (unless problem explicitly says to).
a) How many ways are there to choose the Exec Board from all Rackham students?
b) How many ways are there to choose the Exec Board so that there is at least one masters student and one PhD student? (for any of the 4 positions)
c) How many ways are there to choose the Exec Board if the VP positions have to be PhD students (the president can be either a PhD or Masters student)?
d) How many ways are there to choose the Exec Board so that there is at least one masters student VP?
Answer:
a) 8,000!/(8000 - 4)! ways
b) 15,000,000 + 7998!/(7998 - 2)! ways
c) 5,000 + 7,999!/(7,999- 3)! ways
d) 3,000 + 7,999!/(7,999- 3)! ways
Step-by-step explanation:
The number of students at Rackham Graduate School = 8,000 students
The number of PhD students = 5,000
The number of masters students = 3,000
The number of student members of the Rackham Student Government Executive Board = 4 students
a) The number of ways there are to choose the Exec Board from all Rackham students = The number of ways to choose 4 students from 8,000 = 8,000!/(8000 - 4)!
b) The number of ways of having one Master student in the board = 3,000 ways
The number of ways of having one PhD student in the board after selecting a masters student = 5,000 ways
The number of ways of selecting the remaining 2 members =
7998!/(7998 - 2)!
The total number of ways of selecting at least one masters and one PhD in the board is therefore equal to 5,000 × 3,000 + 7998!/(7998 - 2)! ways
c) The number of ways of choosing the VP position as PhD = 5,000 ways
The number of ways of choosing the other three members = 7,999!/(8000 - 3)!
Therefore, the total number of ways = 5,000 + 7,999!/(7,999- 3)! ways
d) The number of ways of choosing a masters student as the VP position = 3,000 ways
The number of ways of choosing the other three members = 7,999!/(8000 - 3)!
Therefore, the total number of ways = 3,000 + 7,999!/(7,999- 3)! ways
Write the fraction 28 in its simplest form.
70
Answer: 2/5
Step-by-step explanation: 28/70 ÷ 12/12 = 2/5
The simplest form of the given fraction is 2 / 5
What is a fraction?A fraction represents part of a whole. When something is broken up into a number of parts, the fraction shows how many of those parts you have.
Given is a fraction, 28 / 70, we have to convert it into its simplest form,
28 / 70
= 2(14) / 5(14)
= 2 / 5
Hence, the simplest form of the given fraction is 2 / 5
For more references on fractions, click;
https://brainly.com/question/10354322
#SPJ2
1) f(x) = 3*
f(x)
x
-1
0
1
2 3
1)f(×)=3*=f(×)=×-1 0 1=0.23
identify the coefficeient following expression
6a+7
Answer:
6
Step-by-step explanation:
The coeffecient is the number next to the variable. Boom. Done.
Answer:
6
Step-by-step explanation:
a coefficient is a number in front (behind) the variable (ex. the coefficient in 2x is 2, and the variable is x)
i hope this helps :)
How many joules of gravitational potential energy are stored in an object that has a mass of 8.5 kilograms and is held 2 meters above the surface of earth?
Answer:
I believe the answer is 166.6 Joules or (if rounding to the nearest whole number) 167 Joules.
Step-by-step explanation:
Here is the formula to find the gravitational potential energy of an object:
U = m * g * h (potential energy equals mass times gravitational acceleration * the height)
The mass is 8.5 kilograms, the height is 2 meters, and Earth's gravitational acceleration is always, no matter the other values or earthly situations, 9.8 m/s.
Now we solve:
8.5 * 9.8 * 2 = 166.6 which is rounded to 167 Joules.
Write 8 1/5 as a fraction
Answer:
8.2
Step-by-step explanation:
let me know if its wrong
Solve for x Enter the solutions from least to greatest . (x - 4)(- 5x + 1) = 0 lesser x = greater x =
Answer: lesser x = 1/5 greater x = 4
Step-by-step explanation:
A researcher studies differences in career goals between boys and girls in middle school. All of the students in the seventh grade schools in a particular county answer a list of questions. What type of study is this?
A. Experiment
B. Sample Survey
C. Observational Study
D. Random Trial
Explanation:
When asking/answering questions like this, a survey is involved. It could be multiple choice or fill in the blank. Multiple choice may be the best way because it's easier to compare data results when you have only a few options. It also gives the computer an easier time too.
We aren't conducting an experiment since the researcher is not directly affecting the people, and instead letting them answer the questions without intervention. Also, note how we don't have two groups of treatment vs control. This is another indication we don't have an experiment.
An observational study is not being done here either. Yes the researcher is observing the survey results, but s/he is not making notes on the individuals before the survey is conducted (ie before the questions are asked). An example of an observational study is having the researcher make a tally of students' hair color. The researcher simply looks at each student, marks the correct tally, and doesn't need to ask the student a question. So you can see that the interactive question/answer portion is not present in an observational study.
The phrasing "random trial" is not a study type. When you hear "random trial" in the news, maybe for a new drug being developed, the news report is implying heavily that an experimental study had been done. This is true with all drug trials. One group is the treatment group that gets the actual drug, while the control group gets a fake drug. The control group thinks they get the actual drug, which is important because if they knew it was fake, then it would invalidate the study. I recommend researching the placebo affect for more information. The two group's results are then computed to see if the drug did in fact cause a change in the subjects or not. You would see this if there's a significant difference between the treatment and control group. Anyway, the "random trial" is not a study type but rather an aspect of an experimental study. It's possible your teacher put this in here to throw off students.
What is the value of c so that −15 and 15 are both solutions of x^2−c=157?
Answer: -c= 157+X^2
Step-by-step explanation:
How can you find f(4) if f(x)=7x^(2)-5
Answer:
107
Step-by-step explanation:
f(x)=7x^(2)-5
f(4) means that x=4
f(4)=7*4^(2)-5
= 7 * 16 -5
= 112 -5
= 107
What is the slope of a line of best fit if its equation is y = −2x + 3?
−2
Negative 1 over 2
1 over 3
3
Answer:
-2
Step-by-step explanation:
y=m(slope)x+b(y axis)
An electronics store is having a 15% off sale. Suppose the sale price(p) of a laptop is $495. Which statement are true for this stuation
A. P+ 0.15p represents the sales price
B. P- 0.15p represent the sales price
C. 0.85p represents the sales price
D. The sale price is 420.75
E. The sale price is 569.25
Answer:
The answer to the Question is D
Answer:
B, C, D
Step-by-step explanation:
If the sales price is 15% off, then the the price is .85(100-15%) of the price so c is true
this also makes b true. (100-15%) is p-.15
495 x .85 (100-15%)=420.75 so d is true
Jose Luis desea colocar una línea de azulejos alrededor de toda la piscina de su casa. La piscina tiene forma rectangular con un ancho de 10 m y una longitud de 25 m. , ¿cuántos metros lineales de azulejos necesitará comprar?
Answer:
70
Step-by-step explanation:
2 x (25 + 10) = 2 x 35 = 70
Jeff and George each have a box of popcorn. How much more popcorn does the bigger box hold than the smaller box?
Answer:
there in not enough information in your question to get an answer
Answer:
Part 1: Jeff Part 2: 130
Step-by-step explanation:
What is 3r-2 ?? Algebra is not my strong suit
What is the distance between point (5, 9) and its reflection across the x-axis?
Answer:
10 units
Step-by-step explanation:
You are traveling down a country road at a rate of 95 feet/sec when you see a large cow 300 feet in front of you and directly in your lane. The cow is fearless, and staring you down. (Or perhaps she does not understand the gravity of the situation.) Regardless, if you simply hit your brakes, after t seconds, the car will be j(t) = 95t - 9t^2 feet from the point where the brakes were first applied.
1) Must you steer to avoid the cow, or can you rely solely on your brakes? Explain.
2) Graph J(t), j'(t), and j"(t) and Interpret their meanings in context.
3) Is there a time t after which the graphs in part (ii) probably do not accurately model the path of the car?
4) Write a piece-wise function using j(t) that would more accurately model the path of the car on the interval [0, 10], assuming the car did not move after it stopped. Sketch this graph and its derivative.
Answer:
1) You can rely solely on your brakes because when doing so the car will just travel 250ft from the point you hit your brakes till the point the car stopped completely, leaving you 50ft away from the cow.
2) See attached picture.
j(t) represents the distance from the point you hit the brake t seconds after you hit it in feet
j'(t) represents the velocity of the car t seconds after the brakes have been hit in ft/s.
j"(t) represents the acceleration of the car t seconds after the brakes have been hit in [tex]ft/s^{2}[/tex]
3) yes, any time after t=5.28 will not accurately model the path of the car since at that exact time the car will reach a velocity of 0ft/s and unless another force is applied to the car, then the car will not move after that time.
4) [tex]j(t)=\left \{ {{95t-9t^{2}; 0\le t<5.28s} \atop {250.69; 5.28s\leq t \leq 10s}} \right.[/tex]
[tex]j'(t)=\left \{ {{95-18t; 0\leq t<5.28s} \atop {0 ; 5.28s\leq t \leq 10s}} \right.[/tex]
(see attached picture for graph)
Step-by-step explanation:
1) In this part of the problem we need to find the time when the speed of the car is 0. Gets to a complete stop. For this we will need to take the derivative of the position function so we get:
[tex]j(t)=95t-9t^2[/tex]
[tex]j'(t)=95-18t[/tex]
and we set the first derivative equal to zero so we get:
95-18t=0
and solve for t
-18t=-95
[tex]t=\frac{95}{18}[/tex]
t=5.28s
so now we calculate the position of the car after 5.28 seconds, so we get:
[tex]j(5.28)=95(5.28)-9(5.28)^{2}[/tex]
[tex]j(5.28)=250.69ft[/tex]
so we have that the car will stop 250.69ft after he hit the brakes, so there will be about 50ft between the car and the cow when the car stops completely, so he can rely just on the breaks.
2) For answer 2 I take the second derivative of the function so I get:
[tex]j(t)=95t-9t^{2}[/tex]
[tex]j'(t)=95-18t[/tex]
j"(t)=-18
and then we graph them. (See attached picture)
j(t) represents the distance from the point you hit the brake t seconds after you hit it in feet
j'(t) represents the velocity of the car t seconds after the brakes have been hit in ft/s.
j"(t) represents the acceleration of the car t seconds after the brakes have been hit in [tex]ft/s^{2}[/tex]
3) yes, any time after t=5.28 will not accurately model the path of the car since at that exact time the car will reach a velocity of 0ft/s and unless another force is applied to the car, then the car will not move after that time.
4) [tex]j(t)=\left \{ {{95t-9t^{2}; 0\le t<5.28s} \atop {250.69; 5.28s\leq t \leq 10s}} \right.[/tex]
[tex]j'(t)=\left \{ {{95-18t; 0\leq t<5.28s} \atop {0 ; 5.28s\leq t \leq 10s}} \right.[/tex]
(see attached picture for graph)
Gina tosses a number cube 66 times. About how many times would you expect that Gina would toss a 6?
Answer:11
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
its 11 because 66 divided by 6 = 11
Tanner collected 360 cans and bottles while fundraising for his basketball team This was 40% less than what Reggie collected How many cans and bottles did Reggie collect?
Answer:
Reggie collected 504 cans and bottles.
Step-by-step explanation:
40%=.40
360*.40=144
360+144=504
CL 6-153
In 2012 the average cost for a new midsized car was about
$31,000. New car prices tend to go up about 2% every year.
a. What is the multiplier for this situation?
b. If this trend continues, what will the cost be in 4 years?
c. Write an equation to calculate the cost in n years. What does
each of the factors in your equation represent?
Answer:
A) The multiplier for this situation is 0.02.
B) The cost in 4 years will be $ 33,555.39.
C) 31,000 x 1.02 ^ N = X
Step-by-step explanation:
Since in 2012 the average cost for a new midsized car was about $ 31,000, and new car prices tend to go up about 2% every year, to determine what is the multiplier for this situation, what will the cost be in 4 years if this trend continues and to write an equation to calculate the cost in n years the following calculations must be performed:
A)
31,000 x 2/100 = X
31,000 x 0.02 = X
Thus, the multiplier for this situation is 0.02.
B)
31,000 x 1.02 ^ 4 = X
33,555.39 = X
Thus, the cost in 4 years will be $ 33,555.39.
C)
31,000 x 1.02 ^ N = X
Here, N represents the number of years over which the price increase will be calculated, and X represents the price after that number of years.
The batteries produced in a manufacturing plant have a mean time to failure of 30 months with a standard deviation of 2 months. I select a simple random sample of 400 batteries produced in the manufacturing plant. I test each and record how long it takes for each battery to fail. I then compute the average of all the failure times. The sampling distribution of is approximately:
Answer:
By the Central Limit Theorem, the sampling distribution is approximately normal, with mean 30 and standard deviation 0.1.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
The batteries produced in a manufacturing plant have a mean time to failure of 30 months with a standard deviation of 2 months.
This means that [tex]\mu = 30, \sigma = 2[/tex]
Sample of 400 batteries. The sampling distribution of is approximately:
So [tex]n = 400, s = \frac{\sigma}{\sqrt{n}} = \frac{2}{\sqrt{400}} = 0.1[/tex]
By the Central Limit Theorem, the sampling distribution is approximately normal, with mean 30 and standard deviation 0.1.
What is the slope of the line that goes through (-3, 2) and (3, 2)?
Answer:
m = 0
Step-by-step explanation:
Hope this helps:)
with one of these is a function
a
b
c
d
Answer:
It's B
Step-by-step explanation:
Answer:
B is a functional answer
7
Carly has a bank account with a balance of $3,575. The account pays simple interest at a rate of
4.15%. How long will it take for the account to grow to $7000? Round to the nearest year.
Answer:
It will take 23 years for the account to grow to $7000.
Step-by-step explanation:
Simple Interest
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
[tex]T = E + P[/tex]
Carly has a bank account with a balance of $3,575.
This means that [tex]P = 3575[/tex]
The account pays simple interest at a rate of 4.15%.
This means that [tex]I = 0.0415[/tex]
How long will it take for the account to grow to $7000?
[tex]T = 7000[/tex]
The interest is:
[tex]T = E + P[/tex]
[tex]E = T - P = 7000 - 3575 = 3425[/tex]
Now we have to find t.
[tex]E = P*I*t[/tex]
[tex]3425 = 3575*0.0415*t[/tex]
[tex]t = \frac{3425}{3575*0.0415}[/tex]
[tex]t = 23.1[/tex]
Rounding to the nearest year, it will take 23 years for the account to grow to $7000.
Use the distributive property to simplify the following expression: 3 (2 + 5z)
The length of a cell phone is 1.41.4 inches and the width is 4.44.4 inches. The company making the cell phone wants to make a new version whose length will be 1.751.75 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
Answer:
Step-by-step explanation:
Answer:
5.573.75
Step-by-step explanation:
because math
Gavin needs to buy candy for the 11 students in his class plus himself. Gavin and each student will get one bag of candy. He uses $20 to buy two different types of candy. Gavin buys x bags of gummy bears that cost $1.50 per bag and y bags of chocolates that cost $2.00 per bag. The system of equations used to represent this situation is graphed, as shown.
Answer:
20=1.50(6)+2.00(4)
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Select the correct comparison.
Set A
Set B
.
....
24
8 10
4 6 8 12
A. The typical value and the spread are both greater in set B.
B. The typical value and the spread are both greater in set A.
C. The typical value is greater in set A. The spread is greater in set B.
D. The typical value is greater in set B. The spread is greater in set A.
Answer:i would say C ADHAKFFA
Step-by-step explanation: